Vector Imported curves not moving on Z axis
Using a 2D curve implies that the Local Z coordinate of each control point is 0.



From the Blender manual's page about the topic:


  By default, new curves are set to be 3D, which means that Control Points can be placed anywhere in 3D space. Curves can also be set to 2D which constrain the Control Points to the Curve’s local XY axis.


In a 2D curve you can't even set it's origin's Z coordinate with the 3D cursor. It is forced to lay on the plane where the the control points are.

You should switch the curve nature to 3D to be able to move them up and down.